Question

Demonstrate how you can use the slope formula to write the point-slope form of an equation of a line.

Answer 1

suppose y = mx + b, and suppose (xₒ,yₒ) is on the line. Then,
yₒ = mxₒ + b

subtract to get
y - yₒ = mx - mxₒ

y - yₒ = m(x - xₒ), which is point-slope form

Answer 2

But you @shawn haven't used the slope formula as the question asks?

Answer 3

??? isn't slope formula y = mx + b?

Answer 4

nope, that is the slope-intercept form of an equation of a line.

Answer 5

so what is the slope formula? ax + by + c = 0?

Answer 6

$$\huge m = \dfrac{y_2 - y_1}{x_2 - x_1}$$

Answer 7

That^ is the formula for the slope of a line.

Answer 8

ohhh.....

To the asker: in which case just replace y2 with y and x2 with y, and solve for y - y1

Answer 9

Provided
$$\huge x_1 \neq x_2$$

Answer 10

Point slope form:
$$\huge y-y_0=m(x-x_0)$$

Answer 11

So multiply both side of the slope formula by $$x_2-x_1$$

Answer 12

note you now have to change the subscripts too ;-)